Othes can chip in and explain in more detail, but I'll give a rough rundown (and at the same time, my own opinion).
1.) Downloading copyrighted games, wether they be CD images or roms is illegal unless the copyright holder has given his/hers explicit permission that the game(s) can be downloaded from the net for free. Public Domain roms are another matter.
2.) You are free to make a backup from a game/games you own, but this doesn't mean that you can legally download the games that you own from the net.
3.) A lot of romsites like to mention the 24-hour rule. That is, you can download a rom from somewhere and keep on your computer for 24 hours. After this you must delete the rom image. This is complete bullshit, and an urban legend of sorts.
4.) Emulators are perfectly legal, provided that they are not bundled with roms and copyrighted BIOS files. If the BIOS is embedded into the emulator, the emulator is illegal.
